Where I used to work, they used to clean PCB pads and pogo pins with alcohol wipes (70%).
Is it fine to clean with such a product since it is not 100% alcohol?
If no, what damage can be done? can it contribute to increase in resistance when applied to the pogo pins?

Remember that when the 70% alcohol evaporates, you have water left on the surface. If the solution gets into the pogo pin, the water could damage the spring (depending on its construction). 100% is definitely the best to use, but given that, I use 91% on all of my electronic cleaning needs. If the wipes are just used to clean the surfaces of the pogo pins and the pcb pad, even if water is left on the surfaces, no increase in resistance will be seen, since the pogo pin should bite into the pcb pad when activated (I'm assuming a castellated or chisel point pin on the pogo).

Yep.. IPA is commonly used as an economical flux remover on soldered circuit board assemblies..
Nothing wrong with using it at all.. As stated a higher percentage will simply have less water (91%,etc...)